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RegularChains[MatrixTools]

  

IsZeroMatrix

  

check whether a matrix is null modulo a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsZeroMatrix(A, rc, R)

Parameters

A

-

square Matrix with coefficients in the ring of fractions of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

The command IsZeroMatrix(A, rc, R) returns true if and only if A is null modulo the saturated ideal of rc.

• 

It is assumed that rc is strongly normalized.

• 

This command is part of the RegularChains[MatrixTools] package, so it can be used in the form IsZeroMatrix(..) only after executing the command with(RegularChains[MatrixTools]).  However, it can always be accessed through the long form of the command by using RegularChains[MatrixTools][IsZeroMatrix](..).

Examples

with(RegularChains): with(ChainTools): with(MatrixTools):

R := PolynomialRing([y, z]);

Rpolynomial_ring

(1)

rc := Empty(R);

rcregular_chain

(2)

rc := Chain([z^4+1, y^2-z^2], rc, R):

Equations(rc, R);

y2z2,z4+1

(3)

m := Matrix([[1, y+z], [0, y-z]]);

m1y+z0yz

(4)

IsZeroMatrix(m, rc, R);

false

(5)

See Also

Chain

Empty

Equations

IsStronglyNormalized

JacobianMatrix

LowerEchelonForm

MatrixInverse

MatrixMultiply

MatrixOverChain

MatrixTools

NormalForm

PolynomialRing

RegularChains